# Theory of the Algebraic Functions of a Complex Variable

Mayer & Müller, 1906 - Algebraic functions - 186 pages

### What people are saying -Write a review

We haven't found any reviews in the usual places.

### Contents

 Introductory 1 CHAPTER 9 CHAPTER IV 16 CHAPTER V 29 Degree of function as related to orders of coincidence at 43 CHAPTER VII 56 CHAPTER VIII 66
 CHAPTER X 91 CHAPTER XI 106 CHAPTER XII 121 The genus and the functions 143 CHAPTER XIV 161 CHAPTER XV 179

### Popular passages

Page 134 - Ni in terms of the new notation represents the number of arbitrary constants involved in the expression of the most general rational function, whose orders of coincidence with the branches of the several cycles corresponding to the various finite values z = ak exceed by — TI*', — .:(2},... — tj...
Page 134 - T{-00' respectively. arbitrary constants involved in the expression of the most general rational function of (z, v), whose orders of coincidence with the branches of the several cycles corresponding to the various finite values z = a,. exceed by ol*', i(2\ . •. o^.
Page 138 - From (2) it is seen that q — s + 1 is the number of arbitrary constants involved in the expression of the most general rational function of (z, «), whose infinities, all of the first order, correspond to points among the q points here in question.
Page 34 - ... are adjoint, we say that the function is adjoint for the value of the variable in question. To say that a rational function of (z, u) is adjoint for a value of the variable z, is evidently equivalent to saying that its orders of coincidence with the branches of the several cycles are greater than...
Page 147 - ... for we have shewn that it is equal to the number of the arbitrary constants involved in the expression of the general integral rational function built on this basis. Employing the notation N? to designate the number of the arbitrary constants involved...
Page 88 - ... as a result of equating to 0 the principal residue in the product (26). On equating to 0 the principal residue in the product (25) we then impose no further conditions on the coefficients ar-.^t~i than those already obtained on equating to 0 the principal residue in the product (21).
Page 126 - What are the necessary and sufficient conditions, which must be satisfied by the coefficients of...
Page 134 - The expression (18) then represents the number of arbitrary constants involved in the expression of the most general rational function...
Page 135 - We may conceive a set of numbers to be associated with each value of the variable, the numbers however being all 0 save in the sets associated with a finite number of values of z. When...
Page 102 - Q — q + ï is the number of arbitrary constants involved in the expression of the most general rational function whose infinities are included under a certain set of Q infinities, Ada matliematira.